To calculate the fundamental frequency of the auditory canal, we need to use the speed of sound and the length of the canal.
The fundamental frequency is the lowest frequency at which a resonance occurs in the auditory canal. In other words, it is the frequency that corresponds to the length of the canal.
The formula for calculating the fundamental frequency of a tube open at one end is given by:
f1 = v / (4L)
Where:
- f1 is the fundamental frequency
- v is the speed of sound
- L is the length of the tube
Given:
v = 343 m/s (speed of sound)
L = 2.775 cm = 0.02775 m (length of the auditory canal)
Plugging the values into the formula, we get:
f1 = 343 / (4 * 0.02775)
Simplifying the equation, we have:
f1 = 343 / 0.111
f1 ≈ 3089 Hz
Therefore, the fundamental frequency of the auditory canal is approximately 3089 Hz.